Geometry and rhetoric: Pascal and the Mathematics of the ideal villa

The tension between geometry and matter, and so between geometry and architecture, has a long philosophical history. This paper traces part of that history, where geometry takes on different roles, as in Robin Evans’ account of that history in his book, The Projective Cast, Architecture and its Three Geometries, i and in Colin Rowe’s essay, ‘The Mathematics of the Ideal Villa’ (1947), on the comparisons between the use of geometry in the work of Palladio and of Le Corbusier.ii Where geometry becomes seen to be a species of rhetoric, is most evident in the writings of Pascal, where geometry and rhetoric are paired. In 1657 or 1658, Pascal wrote two short treatises on the rhetorical function of geometry titled De l’esprit géométrique, and L’Art de persuasion. In these writings, Pascal burdens geometry with the demand that the truth of matter be articulate, and
persuasively demonstrated.